The challenge comes as Cruz escalated his war of words against the Iowa frontruner. Cruz had occasionally been mentioning Trump by name and criticizing him obliquely; he continually hammered on him by name Tuesday night, telling the crowd at an events space here that Trump supports government funding for Planned Parenthood, the Affordable Care Act and painting him as a member of the Washington elite who will cut deals and capitulate to their demands.
Cruz said Trump is "scared" of moderator Megyn Kelly, with whom he sparred during a debate last year and later said she had "blood coming out of her wherever." Cruz kept referring to Trump as "gentle Donald" and called him a "fragile soul."
"She might ask a mean question," Cruz said of Kelly. He suggested other conservative moderators, but said it can be done without any.
"At the end of the day it’s not really that Donald is afraid of Megyn," Cruz said. "He’s afaid if you. He doesn’t want to answer questions form the men and women of Iowa about how his record doesn’t match what he’s selling."
Cruz said Trump lacks the humility and judgment to be the next president, and said the country has spent seven years with a "narcissitic, self-involved" president for seven years, and shouldn't elect another.
A spokeswoman for Trump didn't immediately respond to a request for comment.
The Texas Republican also took his hardest shots at Trump for a variety of issues, including health care.
"If Donald Trump is elected president he intends to expand Obamacare," he said. "Trumpcare is socialized medicine."
Cruz said that Trump supports the taxpayer funding of Planned Parenthood and has said he is pro-choice.
"If we nominate and elect a president who spent the first 60 years of his life supporting partial birth abortion we should not be surprised when we see the Supreme Court justices that president puts on the court," Cruz said.
A constellation of super PACs supporting Cruz offered to pledge $1.5 million to charities if Trump debates Cruz one-on-one before Sunday.